Subgroups — C₁₉×#19771 #18025730

Order 4864.

736 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1717	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1701	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1639	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1629	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1624	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₁₉	—	2	1	no	—
17	C₁₉×#555	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
19	D₄²×C₁₉	C₂²	1	1	yes	characteristic
20	D₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#493	C₂²	1	1	yes	characteristic
22	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#485	—	2	1	no	—
28	C₁₉×#482	—	2	1	no	—
29	C₁₉×#480	—	2	1	no	—
30	C₁₉×#476	C₂²	1	1	yes	characteristic
31	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#474	C₂²	1	1	yes	characteristic
33	C₁₉×#469	—	2	1	no	—
34	C₁₉×#466	—	2	1	no	—
35	C₁₉×#466	—	2	1	no	—
36	C₁₉×#465	—	2	1	no	—
37	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#459	C₂²	1	1	yes	characteristic
39	C₁₉×#459	C₂²	1	1	yes	characteristic
40	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#449	—	2	1	no	—
43	C₁₉×#447	—	2	1	no	—
44	C₁₉×#447	—	2	1	no	—
45	C₁₉×#447	—	2	1	no	—
46	C₁₉×#447	—	2	1	no	—
47	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
50	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
52	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#418	—	2	1	no	—
54	C₁₉×#416	—	2	1	no	—
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	4	1	no	—
74	C₂×D₈×C₁₉	—	2	1	no	—
75	C₂×D₈×C₁₉	—	2	1	no	—
76	C₂×D₈×C₁₉	—	2	1	no	—
77	C₂×D₈×C₁₉	—	2	1	no	—
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×D₈×C₁₉	—	2	1	no	—
80	C₂×D₈×C₁₉	—	4	4	no	—
81	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
82	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
83	C₂×M₁₆×C₁₉	—	2	1	no	—
84	C₂²×C₈×C₁₉	—	2	1	no	—
85	C₂²×C₈×C₁₉	—	2	1	no	—
86	C₂²×C₈×C₁₉	—	2	1	no	—
87	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₉×#127	C₂³	1	1	yes	characteristic
90	C₁₉×#127	C₂³	1	1	yes	characteristic
91	C₁₉×#124	—	4	1	no	—
92	C₁₉×#123	—	4	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#120	—	4	1	no	—
102	C₁₉×#120	—	4	1	no	—
103	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₁₉×#107	—	2	1	no	—
111	C₁₉×#107	D₄	1	1	yes	characteristic
112	C₁₉×#107	D₄	1	1	yes	characteristic
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×#103	—	2	1	no	—
120	C₁₉×#103	—	2	1	no	—
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#102	—	2	1	no	—
123	C₁₉×#102	—	2	1	no	—
124	C₁₉×#102	—	2	1	no	—
125	C₁₉×#102	—	2	1	no	—
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	4	1	no	—
134	C₁₉×#102	D₄	1	1	yes	characteristic
135	C₁₉×#102	D₄	1	1	yes	characteristic
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₂⁴×C₁₉	—	4	1	no	—
146	C₂⁴×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	2	no	—
148	#41×C₁₉	—	8	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	4	1	no	—
158	C₂×D₄×C₁₉	—	4	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	—	4	2	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	—	4	1	no	—
167	C₂×D₄×C₁₉	—	8	1	no	—
168	C₂×D₄×C₁₉	—	8	1	no	—
169	C₂×D₄×C₁₉	—	8	1	no	—
170	C₂×D₄×C₁₉	—	8	1	no	—
171	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	4	1	no	—
180	SD₁₆×C₁₉	—	8	1	no	—
181	SD₁₆×C₁₉	—	8	2	no	—
182	D₈×C₁₉	—	2	2	no	—
183	D₈×C₁₉	—	2	2	no	—
184	D₈×C₁₉	—	4	2	no	—
185	D₈×C₁₉	—	4	2	no	—
186	D₈×C₁₉	—	4	2	no	—
187	D₈×C₁₉	—	8	1	no	—
188	D₈×C₁₉	—	8	1	no	—
189	D₈×C₁₉	—	8	1	no	—
190	M₁₆×C₁₉	—	8	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	4	2	no	—
197	C₂×C₈×C₁₉	—	8	1	no	—
198	C₂×C₈×C₁₉	—	8	1	no	—
199	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	4	1	no	—
208	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	4	1	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₂²⋊C₄×C₁₉	—	4	1	no	—
219	C₂²⋊C₄×C₁₉	—	4	1	no	—
220	C₂²⋊C₄×C₁₉	—	4	1	no	—
221	C₄²×C₁₉	—	4	1	no	—
222	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
223	#19771	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	8	2	no	—
231	C₂³×C₁₉	—	8	2	no	—
232	C₂³×C₁₉	—	8	2	no	—
233	C₂³×C₁₉	—	8	2	no	—
234	C₂³×C₁₉	—	16	1	no	—
235	C₂³×C₁₉	—	16	1	no	—
236	Q₈×C₁₉	—	4	1	no	—
237	Q₈×C₁₉	—	4	1	no	—
238	Q₈×C₁₉	—	8	1	no	—
239	D₄×C₁₉	—	2	1	no	—
240	D₄×C₁₉	—	2	1	no	—
241	D₄×C₁₉	—	2	1	no	—
242	D₄×C₁₉	—	2	1	no	—
243	D₄×C₁₉	—	2	1	no	—
244	D₄×C₁₉	—	2	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	4	1	no	—
252	D₄×C₁₉	—	4	1	no	—
253	D₄×C₁₉	—	8	1	no	—
254	D₄×C₁₉	—	8	1	no	—
255	D₄×C₁₉	—	8	2	no	—
256	D₄×C₁₉	—	8	2	no	—
257	D₄×C₁₉	—	8	2	no	—
258	D₄×C₁₉	—	8	2	no	—
259	D₄×C₁₉	—	8	2	no	—
260	D₄×C₁₉	—	16	1	no	—
261	D₄×C₁₉	#135	1	2	yes	—
262	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	8	2	no	—
278	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
281	C₈×C₁₉	—	2	1	no	—
282	C₈×C₁₉	—	2	1	no	—
283	C₈×C₁₉	—	2	1	no	—
284	C₈×C₁₉	—	2	1	no	—
285	C₈×C₁₉	—	4	1	no	—
286	C₈×C₁₉	—	4	1	no	—
287	C₈×C₁₉	—	4	1	no	—
288	C₈×C₁₉	—	4	1	no	—
289	C₈×C₁₉	—	4	1	no	—
290	#3325	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#3303	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#3294	C₂×C₁₉	1	1	yes	characteristic, complemented
293	D₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1717	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1701	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1683	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1667	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1639	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1629	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1625	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1624	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1580	C₂×C₁₉	1	1	yes	characteristic, complemented
305	C₂²×C₁₉	—	2	2	no	—
306	C₂²×C₁₉	—	2	2	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	—	4	1	no	—
310	C₂²×C₁₉	—	4	1	no	—
311	C₂²×C₁₉	—	4	1	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	1	no	—
314	C₂²×C₁₉	—	4	1	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	—	4	1	no	—
317	C₂²×C₁₉	—	8	1	no	—
318	C₂²×C₁₉	—	8	1	no	—
319	C₂²×C₁₉	—	8	1	no	—
320	C₂²×C₁₉	—	8	1	no	—
321	C₂²×C₁₉	—	8	1	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	—	16	4	no	—
324	C₂²×C₁₉	—	16	4	no	—
325	C₂²×C₁₉	D₄²	1	1	yes	characteristic
326	C₄×C₁₉	—	2	1	no	—
327	C₄×C₁₉	—	4	1	no	—
328	C₄×C₁₉	—	4	1	no	—
329	C₄×C₁₉	—	4	1	no	—
330	C₄×C₁₉	—	4	1	no	—
331	C₄×C₁₉	—	8	1	no	—
332	C₄×C₁₉	—	8	1	no	—
333	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
334	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
335	C₄×C₁₉	#576	1	1	yes	characteristic
336	C₄×C₁₉	#576	1	1	yes	characteristic
337	C₂²×D₈	—	2	1	no	—
338	#555	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
340	D₄²	C₂²×C₁₉	1	1	yes	characteristic
341	D₄²	C₂²×C₁₉	1	1	yes	characteristic
342	#493	C₂²×C₁₉	1	1	yes	characteristic
343	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
344	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
345	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
346	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
347	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
348	#485	—	2	1	no	—
349	#482	—	2	1	no	—
350	#480	—	2	1	no	—
351	#476	C₂²×C₁₉	1	1	yes	characteristic
352	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	#474	C₂²×C₁₉	1	1	yes	characteristic
354	#469	—	2	1	no	—
355	#466	—	2	1	no	—
356	#466	—	2	1	no	—
357	#465	—	2	1	no	—
358	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
359	#459	C₂²×C₁₉	1	1	yes	characteristic
360	#459	C₂²×C₁₉	1	1	yes	characteristic
361	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#449	—	2	1	no	—
364	#447	—	2	1	no	—
365	#447	—	2	1	no	—
366	#447	—	2	1	no	—
367	#447	—	2	1	no	—
368	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
369	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
370	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
372	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	#418	—	2	1	no	—
375	#416	—	2	1	no	—
376	C₂×#102	—	2	1	no	—
377	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
378	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
379	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
380	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
381	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
382	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
383	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
384	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
385	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
386	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
387	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
388	C₂×C₁₉	—	4	2	no	—
389	C₂×C₁₉	—	4	2	no	—
390	C₂×C₁₉	—	8	1	no	—
391	C₂×C₁₉	—	8	1	no	—
392	C₂×C₁₉	—	16	1	no	—
393	C₂×C₁₉	—	16	1	no	—
394	C₂×C₁₉	#3264	1	1	yes	characteristic
395	C₂×C₁₉	#3280	1	1	yes	characteristic
396	C₂×C₁₉	#3288	1	1	yes	characteristic
397	C₂×#41	—	2	1	no	—
398	C₂²×D₄	—	2	1	no	—
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂×SD₁₆	—	2	1	no	—
403	C₂×SD₁₆	—	4	1	no	—
404	C₂×D₈	—	2	1	no	—
405	C₂×D₈	—	2	1	no	—
406	C₂×D₈	—	2	1	no	—
407	C₂×D₈	—	2	1	no	—
408	C₂×D₈	—	2	1	no	—
409	C₂×D₈	—	2	1	no	—
410	C₂×D₈	—	4	4	no	—
411	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
412	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
413	C₂×M₁₆	—	2	1	no	—
414	C₂²×C₈	—	2	1	no	—
415	C₂²×C₈	—	2	1	no	—
416	C₂²×C₈	—	2	1	no	—
417	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
419	#127	C₂³×C₁₉	1	1	yes	characteristic
420	#127	C₂³×C₁₉	1	1	yes	characteristic
421	#124	—	4	1	no	—
422	#123	—	4	1	no	—
423	C₂²⋊Q₈	—	2	1	no	—
424	#121	—	2	1	no	—
425	#121	—	2	1	no	—
426	#121	—	2	1	no	—
427	#121	—	2	1	no	—
428	#121	—	2	1	no	—
429	#121	—	2	1	no	—
430	#121	—	2	1	no	—
431	#120	—	4	1	no	—
432	#120	—	4	1	no	—
433	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
434	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
435	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
436	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
437	#117	—	2	1	no	—
438	#117	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	#107	—	2	1	no	—
441	#107	D₄×C₁₉	1	1	yes	characteristic
442	#107	D₄×C₁₉	1	1	yes	characteristic
443	#106	—	2	1	no	—
444	#106	—	2	1	no	—
445	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
449	#103	—	2	1	no	—
450	#103	—	2	1	no	—
451	#103	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	1	no	—
455	#102	—	2	1	no	—
456	#102	—	2	1	no	—
457	#102	—	2	1	no	—
458	#102	—	2	1	no	—
459	#102	—	2	1	no	—
460	#102	—	2	1	no	—
461	#102	—	2	1	no	—
462	#102	—	2	1	no	—
463	#102	—	4	1	no	—
464	#102	D₄×C₁₉	1	1	yes	characteristic
465	#102	D₄×C₁₉	1	1	yes	characteristic
466	#102	D₄×C₁₉	1	1	yes	characteristic
467	#102	D₄×C₁₉	1	1	yes	characteristic
468	C₂²⋊C₈	—	2	1	no	—
469	C₂²⋊C₈	—	2	1	no	—
470	C₂²⋊C₈	—	2	1	no	—
471	C₂²⋊C₈	—	2	1	no	—
472	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
473	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
474	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
475	C₁₉	#19771	1	1	yes	characteristic, direct product factor, Sylow
476	C₂⁴	—	4	1	no	—
477	C₂⁴	—	4	1	no	—
478	#41	—	4	2	no	—
479	#41	—	8	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	4	1	no	—
489	C₂×D₄	—	4	1	no	—
490	C₂×D₄	—	4	1	no	—
491	C₂×D₄	—	4	1	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	4	2	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	4	1	no	—
497	C₂×D₄	—	4	1	no	—
498	C₂×D₄	—	8	1	no	—
499	C₂×D₄	—	8	1	no	—
500	C₂×D₄	—	8	1	no	—
501	C₂×D₄	—	8	1	no	—
502	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	4	1	no	—
511	SD₁₆	—	8	1	no	—
512	SD₁₆	—	8	2	no	—
513	D₈	—	2	2	no	—
514	D₈	—	2	2	no	—
515	D₈	—	4	2	no	—
516	D₈	—	4	2	no	—
517	D₈	—	4	2	no	—
518	D₈	—	8	1	no	—
519	D₈	—	8	1	no	—
520	D₈	—	8	1	no	—
521	M₁₆	—	8	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	4	2	no	—
528	C₂×C₈	—	8	1	no	—
529	C₂×C₈	—	8	1	no	—
530	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
533	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
540	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₂²⋊C₄	—	4	1	no	—
550	C₂²⋊C₄	—	4	1	no	—
551	C₂²⋊C₄	—	4	1	no	—
552	C₄²	—	4	1	no	—
553	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	8	2	no	—
561	C₂³	—	8	2	no	—
562	C₂³	—	8	2	no	—
563	C₂³	—	8	2	no	—
564	C₂³	—	16	1	no	—
565	C₂³	—	16	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	8	1	no	—
569	D₄	—	2	1	no	—
570	D₄	—	2	1	no	—
571	D₄	—	2	1	no	—
572	D₄	—	2	1	no	—
573	D₄	—	2	1	no	—
574	D₄	—	2	1	no	—
575	D₄	—	4	1	no	—
576	D₄	—	4	1	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	D₄	—	8	1	no	—
584	D₄	—	8	1	no	—
585	D₄	—	8	2	no	—
586	D₄	—	8	2	no	—
587	D₄	—	8	2	no	—
588	D₄	—	8	2	no	—
589	D₄	—	8	2	no	—
590	D₄	—	16	1	no	—
591	D₄	C₁₉×#135	1	2	yes	—
592	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	8	2	no	—
608	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
610	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
611	C₈	—	2	1	no	—
612	C₈	—	2	1	no	—
613	C₈	—	2	1	no	—
614	C₈	—	2	1	no	—
615	C₈	—	4	1	no	—
616	C₈	—	4	1	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₈	—	4	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	8	1	no	—
633	C₂²	—	8	1	no	—
634	C₂²	—	8	1	no	—
635	C₂²	—	8	1	no	—
636	C₂²	—	8	1	no	—
637	C₂²	—	8	1	no	—
638	C₂²	—	16	4	no	—
639	C₂²	—	16	4	no	—
640	C₂²	D₄²×C₁₉	1	1	yes	characteristic
641	C₄	—	2	1	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	8	1	no	—
647	C₄	—	8	1	no	—
648	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
649	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
650	C₄	C₁₉×#576	1	1	yes	characteristic
651	C₄	C₁₉×#576	1	1	yes	characteristic
652	C₂	—	4	2	no	—
653	C₂	—	4	2	no	—
654	C₂	—	8	1	no	—
655	C₂	—	8	1	no	—
656	C₂	—	16	1	no	—
657	C₂	—	16	1	no	—
658	C₂	C₁₉×#3264	1	1	yes	characteristic
659	C₂	C₁₉×#3280	1	1	yes	characteristic
660	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉×#3325	C₂	semidirect
2. C₁₉×#3303	C₂	semidirect
3. C₁₉×#3294	C₂	semidirect
4. D₄×D₈×C₁₉	C₂	semidirect
5. C₁₉×#1717	C₂	semidirect
6. C₁₉×#1701	C₂	semidirect
7. C₁₉×#1683	C₂	semidirect
8. C₁₉×#1677	C₂	semidirect
9. C₁₉×#1667	C₂	semidirect
10. C₁₉×#1639	C₂	semidirect
11. C₁₉×#1629	C₂	semidirect
12. C₁₉×#1625	C₂	semidirect
13. C₁₉×#1624	C₂	semidirect
14. C₁₉×#1581	C₂	semidirect
15. C₁₉×#1580	C₂	semidirect
17. C₁₉×#555	C₂²	semidirect
18. C₁₉×#547	C₂²	semidirect
22. C₁₉×#492	C₂²	semidirect
23. C₁₉×#487	C₂²	semidirect
24. C₁₉×#486	C₂²	semidirect
25. C₁₉×#486	C₂²	semidirect
26. C₁₉×#486	C₂²	semidirect
31. C₁₉×#476	C₂²	semidirect
37. C₁₉×#461	C₂²	semidirect
40. C₁₉×#459	C₂²	semidirect
41. C₁₉×#459	C₂²	semidirect
49. C₁₉×#436	C₂²	semidirect
51. C₈×D₄×C₁₉	C₂²	semidirect
52. C₈×D₄×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#333	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
60. C₁₉×#331	C₂²	semidirect
61. C₁₉×#331	C₂²	semidirect
63. C₁₉×D₄⋊C₈	C₂²	semidirect
64. C₁₉×D₄⋊C₈	C₂²	semidirect
65. C₁₉×D₄⋊C₈	C₂²	semidirect
66. C₁₉×#322	C₂²	semidirect
223. #19771	C₁₉	direct (N × H)
290. #3325	C₂×C₁₉	semidirect
291. #3303	C₂×C₁₉	semidirect
292. #3294	C₂×C₁₉	semidirect
293. D₄×D₈	C₂×C₁₉	semidirect
294. #1717	C₂×C₁₉	semidirect
295. #1701	C₂×C₁₉	semidirect
296. #1683	C₂×C₁₉	semidirect
297. #1677	C₂×C₁₉	semidirect
298. #1667	C₂×C₁₉	semidirect
299. #1639	C₂×C₁₉	semidirect
300. #1629	C₂×C₁₉	semidirect
301. #1625	C₂×C₁₉	semidirect
302. #1624	C₂×C₁₉	semidirect
303. #1581	C₂×C₁₉	semidirect
304. #1580	C₂×C₁₉	semidirect
338. #555	C₂²×C₁₉	semidirect
339. #547	C₂²×C₁₉	semidirect
343. #492	C₂²×C₁₉	semidirect
344. #487	C₂²×C₁₉	semidirect
345. #486	C₂²×C₁₉	semidirect
346. #486	C₂²×C₁₉	semidirect
347. #486	C₂²×C₁₉	semidirect
352. #476	C₂²×C₁₉	semidirect
358. #461	C₂²×C₁₉	semidirect
361. #459	C₂²×C₁₉	semidirect
362. #459	C₂²×C₁₉	semidirect
370. #436	C₂²×C₁₉	semidirect
372. C₈×D₄	C₂²×C₁₉	semidirect
373. C₈×D₄	C₂²×C₁₉	semidirect
377. #335	C₂²×C₁₉	semidirect
378. #334	C₂²×C₁₉	semidirect
379. #333	C₂²×C₁₉	semidirect
380. #332	C₂²×C₁₉	semidirect
381. #331	C₂²×C₁₉	semidirect
382. #331	C₂²×C₁₉	semidirect
384. D₄⋊C₈	C₂²×C₁₉	semidirect
385. D₄⋊C₈	C₂²×C₁₉	semidirect
386. D₄⋊C₈	C₂²×C₁₉	semidirect
387. #322	C₂²×C₁₉	semidirect
475. C₁₉	#19771	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3325	2
C₁₉×#3303	2
C₁₉×#3294	2
D₄×D₈×C₁₉	2
C₁₉×#1717	2
C₁₉×#1701	2
C₁₉×#1683	2
C₁₉×#1677	2
C₁₉×#1667	2
C₁₉×#1639	2
C₁₉×#1629	2
C₁₉×#1625	2
C₁₉×#1624	2
C₁₉×#1581	2
C₁₉×#1580	2
#19771	19

Subgroups — C19×#19771 #18025730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19771 #18025730